3. Consider the following LP: maxz = s.t; z 1 0 0 0 S, S2 and...

Transcribed Image Text:

3. Consider the following LP: maxz = s.t; z 1 0 0 0 S₁, S2 and 53 are the slack variables of the first, second and third constraints, respectively. You are given the fact that the basic variables in the optimal solution are BV = {X2, X3, S1}. x₁ - x₂ + 2x3 x₁ + x₂ + 3x3 ≤ 15 (First constraint) 2x₁x2 + x3 ≤ 2 - (Second constraint) (Third constraint) a. Write down the dual problem. b. Use complementary slackness to fill the following optimal table of the primal LP. X1 -x₁ + x₂ + x3 ≤4 X1, X2, X3 20 1 1/2 -3/2 x2 0 0 X3 0 I 0 $1 0 0 S2 -1 1/2 -1/2 $3 -2 1/2 1/2 Rhs 3. Consider the following LP: maxz = s.t; z 1 0 0 0 S₁, S2 and 53 are the slack variables of the first, second and third constraints, respectively. You are given the fact that the basic variables in the optimal solution are BV = {X2, X3, S1}. x₁ - x₂ + 2x3 x₁ + x₂ + 3x3 ≤ 15 (First constraint) 2x₁x2 + x3 ≤ 2 - (Second constraint) (Third constraint) a. Write down the dual problem. b. Use complementary slackness to fill the following optimal table of the primal LP. X1 -x₁ + x₂ + x3 ≤4 X1, X2, X3 20 1 1/2 -3/2 x2 0 0 X3 0 I 0 $1 0 0 S2 -1 1/2 -1/2 $3 -2 1/2 1/2 Rhs

Answer rating: 100% (QA)

a Solution Primal is MAX Zx x1 x2 2 x3 subject to x1 x2 3 x3 15 2 x1 x2 ... View the full answer